Table of Contents

lochfobbingMechanics

Oct 30, 2013 (3 years and 9 months ago)

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i

Table of Contents


Executive Summary

................................
................................
................................
.......................

ii

Towards A Methodology for the Characterization of Fire Resistive Materials with Respect
to Thermal Perform
ance Models
................................
................................
.........

1

A methodology for characterizing fire resistive materials (FRMs) with respect to thermal performance
models is presented.

Properties that must be
assess
ed include thermal conductivity, heat capacity,
density, an
d enthalpies of reaction
s and phase changes
.

Experimental and computational techniques for
quantifying each of these properties are recommended.


Microstructure and Materials Science of Fire Resistive Materials

................................
........

13

The application of x
-
ray microtomography to characterizing the three
-
dimensional microstructure of
FRMs

is presented.

The
3
-
D

microstructures are analyzed to determine the overall "coarse" porosity and
the size of each individual pore
. This information, along with the microstructure image, can be used to
compute
estimate
s

of
the thermal conductivity

of these composite materials as a function of temperature.


A Slug Calorimeter for Evaluating the Thermal

Performance of Fire Resistive Materials

22

The design, development, and evaluation of a simple slug calorimeter for evaluating the high temperature
thermal conductivity of fire resistive materials
are

presented.

The presente
d test method provides
effective thermal conductivities in the temperature range from 30
o
C to about 700
o
C
,

and through the use
of multiple heating/cooling cycles also provides critical information on the influences of reactions and the
convective transpo
rt of reaction gases on the measured effective thermal conductivity.


Critical and Subcritical Adhesion Measurements of a Model Epoxy Coating Exposed to
Moisture Using the Shaft
-
Loaded Blister Test

................................
.................

36

A novel test method for adhesive coatings is presented. The shaft
-
loaded blister test

(SLBT)

employs a
fracture mechanics
-
based approach, rather than a strength
-
based approach (pull
-
off and lap shear), to
characterize the adhesion of materials.

A
fracture mechanics
-
based approach is advantageous because it
explores adhesive failure mechanisms observed in the actual application of the adhesive as well as
providing enginee
r
ing parameters for

the design of adhesive joints and coatings.


Influence of Experimental Set
-
up and Plastic Deformation on the Shaft
-
loaded Blister Test
................................
................................
................................
...............................

51

The viability of using the
SLBT

as a test method for measuring the adhesion and mechanical properties of
thin films

and coatings is explored.

E
vidence is presented that the SLBT is relatively insensitive to the
effects of plastic deformation that often affect conventional adhesion test methods such as the peel test.


Comparison of Subcr
itical Adhesion Test Methods: The Shaft
-
loaded Blister Test vs. the
Wedge Test
................................
................................
................................
...........

70

This work is part of the ongoing effort to develop the shaft
-
loaded blister test into a
n

adhesion test
method that engineers and scientists can
use for the design of adhesive joints and coatings.
Here, w
e
compare the results from the SLBT with the more conventional double cantilever beam wedge test.



Appendix A. Project Listing for BFRL Research and Development f
or the Safety of
Threatened Buildings Program

................................
................................
.........

77


ii

Executive Summary


As part of its Research and Development for the Safety of Threatened B
uildings Program
(see Appendix A)
, the Building a
nd Fire Research Laboratory (BFRL) at the National Institute of
Standards and Technology (NIST) has initiated a research project on fire resistive materials

(FRMs)

for structural steel
.

This report summarizes the research performed in this program
during
2004. The ongoing WTC investigation has highlighted the criticality of the performance
of
FRM
s during a fire or multi
-
hazard
exposure. Both the adhesion and the thermal performance
of the FRMs are paramount for successfully protecting the steel from fa
il
ure due to loss of
its
mechanical properties
when its

temperature rise
s

beyond
some

critical level (around 500
o
C). As
with any material, it is the underlying microstructure of the FRM that must b
e engineered to
control the thermal and adhesion properties

of the final product. With these considerations in
mind, initial BFRL/NIST research on these materials has focused on a three prong approach
,
characterizing the
microstructure
,
adhesion
, and
thermal properties

of these materials.
As is
illustrated by th
e papers included in this report, b
oth computational and experimental
methodologies are under development. The ultimate goal is to provide the industry with the
measurement and computational tools to make better de
cisions during their materials’
developme
nt and optimization processes, and ultimately to produce better, safer, and more
reliable
fire resistive
materials.


O
n July

14,

2005, a meeting with industry representatives will be held at NIST to explore
the possibility of creating a NIST/industry conso
rtium on Fire Resistive Materials to further
advance the goals of this research program.

Interested parties may contact any of the three
project investigators: Dale Bentz (
dale.bentz@nist.gov
), Emmett O’Brien
(
emmett.obrien@nist.gov
), or Christopher White (
christopher
.
white@nist.gov
).



1

Submitted to Fire and Materials (2004)

Towards
A Methodology for
the
Characteriz
ation of Fire
Resistive

Materials with Respect
to Thermal Performance Models


Dale P. Bentz, Kuldeep R. Prasad, Jiann
C. Yang

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899
-
8615

E
-
mail:
dale.bentz@nist.gov

Phone

: (301) 975
-
5865

Fax

: (301) 990
-
6891


Abstract



A metho
dology is proposed for the characterization of fire
resistive

materials with respect
to thermal performance models. Typically in these models, materials are characterized by their
densities, heat capacities, thermal conductivities, and any enthalpies
(
of
reaction or phase
changes
)
. For true performance modeling, these
thermophysical
properties need to

be
determined as a function of temperature for a wide temperature range from room temperature to
over 1000
o
C. Here, a combined experimental/theoretical/mo
deling approach is proposed for
providing these critical input parameters.

Particularly, the relationship between the three
-
dimensional micr
ostructure of the fire resistive

materials and their thermal conductivities is
highlighted.


Introduction


As progr
ess is made in the integration of structural and fire performance models for
structural steel, one key component is a proper and accurate characterization of the
thermop
hysical

properties of the fire
resistive

materials

(F
R
M)
. To predict the surface
tempe
ratures of the steel and its subsequent mechanical performance, an understanding of the
energy transfer from the fire to the steel through the
F
R
M

is paramount. The four major
thermophysical

properties needed
to model the thermal performance o
f the F
R
Ms
a
re:
density
,
heat capacity, thermal conductivity, and enthalp
y

(
of reactions and phase changes
)
. Furthermore,
these properties are needed as a function of temperature
,

fr
om room temperature to
temperatures
greater than

1000
o
C. In this paper, various app
roaches for obt
aining these data are reviewed

and
critiqued. It appears that a combination of experimental measurements and theoretical/modeling
computations will provide the most robust and accurate characterization for these materials.
While the mechan
ical integrity and adhesion properties
of the FR
Ms

as a function of temperature
are also critical to successful performance during a fire exposure, they will not be c
onsidered in
this initial study
.


Materials



Representative
samples of four spray
-
applied

FR
Ms were obtained from two of the
largest manufacturers in the industry. Two of the materials are

mainly composed of mineral
fibers with a

portland
cement
-
based
binder. The other
two are gypsum
-
based

with either
vermiculite or expanded polystyrene bead
s as lightweight
extenders
.
In the sections that follow,
the materials will be identified only by their binder components, portland cement and gypsum,

2

respectively. T
wo

of the materials

(one portland cement
-
based and one gypsum
-
based)
are
currently avail
able in the U.S. marketplace
,

while the other two were of interest for historical
reasons

and are still in use in various existing structures
. In the latter case, the materials were
supplied by the manufacturers in a condition that matched the historical
materials as closely as
possible. Samples of
both

of the

portland cement
-
based and one of the gypsum
-
based

materials
were sent to a commercial testing laboratory for evaluation of thermal conductivity, heat
capacity, and density (via mass and thermal expa
nsion measurements).
1

In addition, the
materials were characterized by thermogravimetric,
dimensional,
differential scanning
calorimetry, and optical microscopy analysis in the NIST labs.


Properties

Density:


The two contributions to the
dens
ity of any

material are it
s mass and its volume. F
R
Ms
are
complex in that both of these
contributions are changing during a fire exposure.
As
exemplified in Figure
s

1

and 2,

m
ost
F
R
M
s will lose mass in a monotonic fashion during a
high
temperature or
fire exposure
,

due to some combination of dehydration, decarbonation, and
decomposition of organic compounds. Their volume, however, may either increase or decrease.
An increase in volume may be observed as the solid network supporting the F
R
M expands with
increasing

temperature or more dramatically when an intumescent coating foams during thermal
degradation. A decrease in volume may be observed as shrinkage accompanies the mass loss
from this
solid
network.


Figure 1: Example thermogravimetric results for a
gypsum
-
based
spray
-
applied F
R
M

with a
nominal heating rate of 5
o
C/min
. Results are for two nominally identical


50 mg

replicates.

Maximum observed coefficient of variation (COV) for mass loss between the two replicate
samples is 0.9 %.




3

Mass loss can be quantified using thermogravimetric analysis (TGA), as described in
ASTM E1131.
2

Of course, the results will v
ary with the programmed heating rate, sample size,
and sample environment. As shown in Figure 1, spray
-
applied F
R
Ms may lose as much as 25 %
of their initial mass during exposure to 800
o
C. This mass loss also provides critical input for
calculating the
enthalpies of reaction for the in
-
place F
R
M. Once a set of reactions is
hypothesized, the standard heats of reactions may be calculated and normalized by the measured
mass loss to calculate the enthalpy change for the in
-
place material, as will be demonst
rated later
in this paper.


Volume changes (t
hermal expansion
)

can be measured using a dilatometer (ASTM E228)
or interferometry (ASTM E289).
2

High temperature measurements (e.g., >

600
o
C) are often
complicated by the large dimensional changes that may b
e experienced in F
R
Ms, along with
their generally fragile nature. In addition, spray
-
applied materials are inherently anisotropic and
may thus exhibit different coefficients of thermal expansion in the in
-
plane and through
-
thickness dimensions.



Typicall
y, the density at any given temperature is calculated as the ratio of the measured
mass at that temperature to the measured volume at that temperature.


Figure 2: Example thermogravimetric results for a portland cement
-
based
spray
-
applied
F
R
M

with a heatin
g rate of 5
o
C/min
. Results are give
n for two nominally identical

50 mg
replicates.

Maximum observed COV for mass loss between the two replicate samples is 0.4 %.



Heat Capacity:



Two common approaches to estimating heat capacity are to 1) calculate C
p

from a
measurement of thermal diffusivity and knowledge of the de
nsity and thermal conductivity of the
F
R
M, or 2) measure C
p
directly using a differential scanning calorimeter

(DSC)
.
The former is
often complicated by the dynamic nature of F
R
Ms, as they typically lose significant mass during

4

the measurement time.
An e
xciting
recent development for the latter method
is the availability
of commercial simultaneous thermal analysis (STA) units. These units permit the simultaneous
monitoring of heat flow and mass during exposure to a (high) temperature regime. With
conven
tional DSC, only the heat flow is measured and to obtain the specific heat per unit mass of
material

that is the required input for thermal performance models
, the results need to be adjusted
by mass measurements (TGA)
made
on a companion sample. The adva
ntages of making both
measurements simultaneously on the same material specimen
are obvious. In addition
,
newer
commercial STA units may allow for larger
sample
volumes
/masses

(on the order of 1 g as
opposed to
the
50 mg to 100 mg

typical of most DSCs
).
This is especially important for
typical
spray
-
applied
F
R
Ms that
may
exhibit a microstructural heterogeneity on the scale of millimeters.

For F
R
Ms whose mass composition is exactly known, an alternative approach is to calculate the
F
R
M heat capacity as a m
ass
-
weighted average of the heat capacities of the component
materials. Of course, this requires that C
p

data as a function of temperature
are

availa
ble for each
component.



To obtain quantitative C
p

data (via ASTM E1269 for example
2
), the typical proced
ure is
to use a sapphire or other reference specimen to obtain a correction factor (
graciously nam
ed the

calorimetric sensitivity


in the
ASTM
E1269
standard) under the same operating conditions as
those used for the test specimen. Due to typical mass mi
smatch
between

the reference and
sample pans, further corrections may be needed based on the known
tabulated
heat capacities of
aluminum or gold (pans)

as a function of temperature
.

A typical set of DSC curves for a spray
-
applied F
R
M are provided in Figur
e
3
. The presence of several endothermic p
eaks is clearly
indicated. The binder component of this

particular F
R
M is portland cement
-
based and the first
two peaks
(around 100
o
C)
correspond to the loss of
bulk
water
and (loosely) bound water
from
gel
-
like

hydration products

respectively
, the third peak
(near 400
o
C)
to the loss of
chemically
bound
water from calcium hydroxide, and the fourth peak
(near 650
o
C)
most likely to the loss of
carbon dioxide from carbonated reaction products.

This material exhib
ited about a 10 % mass
loss during exposure up to 700
o
C.

By integrating the area under these peaks, the corresponding
enthalpies of reaction could be estimated. However, with the small sample size employed in this
experiment

(< 10 mg)
, a quantitative in
terpretation is hindered by the previously mentioned
heterogeneity of the material, e.g., most likely a representative volume was not sampled in this
specific DSC measurement.


Enthalpies of Reaction:


If the chemical composition of the F
R
M is known, the p
otential exists to calculate the
enthalpies of reaction from heats of formation and heat capacity data.
3
,4

The standard procedure
is to “cool” the reactants down from the reaction temperature to a reference state (temperature)
of 25
o
C, compute the heat o
f reaction at 25
o
C, and then heat the products back up to the
reaction temperature.
4

Here, we will illustrate this simple

procedure for a gypsum
-
based FR
M.
Gypsum, which contains two molecules of water for each molecule of calcium sulfate, undergoes
two

dehydration reactions when exposed to elevated temperatures, first converting to calcium
sulfate hemihydrate and then to the anhydrite form of calcium sulfate. The heat capacities and
heats of formation
(H
f
)
of the relevant compounds are provided in Tabl
e 1.
3
,4

Care must be taken
to consider water in its gas phase form as the reaction temperatures being considered are always
above 100
o
C. Using these properties and the known dehydration reaction stoichiometries (e.g.,


5

Figure 3: Example DSC results (ori
ginal and mass corrected) for a portland cement
-
based
spray
-
applied
F
R
M using gold pans and a sapphire reference.



CaSO
4
-
2H
2
O


CaSO
4
-
0.5H
2
O + 1.5 H
2
O and CaSO
4
-
0.5H
2
O


CaSO
4

+ 0.5 H
2
O), heats of
reaction of 3.01 kJ/g water lost at 150
o
C and 2.35 kJ/
g water lost at 250
o
C are calculated for the
dehydrations to hemihydrate and anhydrite, respectively. These values are in reasonable
agreement with those recently summarized for gypsum plasterboard by Thomas.
5

These values
could then be multiplied by t
he corresponding measured mass loss in these temperature ranges
(from Figure 1 for example) to obtain the enthalpy changes due to reactions for a particular FRM
during fire exposure. Similar calculations can be employed for portland

cement
-
based and
intum
escent FR
Ms, as long as their specific decomposition reactions and corresponding
thermophysical properties
are known.
6
,7

It is worth noting that not all reacti
ons in commercially
available FR
Ms are endothermic in nature, as organic components may provide
significant
exotherms, further supplementing
the energy being provided by a

fire.


Table I. Thermophysical Properties for Gypsum
-
based Compounds at 25
o
C.
3
,4

Compound

Molar mass (g/mol)

C
p

(J
/mol

=
o
C)

H
f

(k
J
/mol)

Gypsum (CaSO
4
-
2H
2
O)

172.17

186.15

-
2024.1

Hemihydrate

(CaSO
4
-
0
.5H
2
O)

145.15

119.5

-
1577.9

Anhydrite (CaSO
4
)

136.14

99.73

-
1435.1

H
2
O

(gas)

18.02

33.62

-
242.01





6

Thermal Conductivity:


A wide variety of experimental techniques exist for measuring the thermal conductivity
of materials at elevat
ed temperatures: high temperature guarded hot plate (ASTM C177), heat
flow meter apparatus (ASTM C518), laser flash diffusivity methods

(ASTM E1461)
, and
transient line
/hot wire

(ASTM C1113) and plane source methods.
2,8
-
10

Similar to the discussion
presen
ted for concrete by Flynn
,
8

these measurements are always complicated by the dynamic
nature of the F
R
M which is undergoing degradation even as its thermal conductivity is being
measured.



An alternative to measuring the thermal conductivities of F
R
Ms at h
igh temperatures is to
measure the value at room temperature (or perhaps up to 100
o
C) and “predict” the higher
temperature value
s

based on some

theory for the conductivity of composite (porous) materials.
Example theories
that are closer to reality than
the simplest parallel and series models
include
those of Russell,
1
1

Frey
,
1
2

and Bruggeman
.
13

For example, the theory of Russell estimates the
thermal conductivity of the porous material,
k
, as
1
1
:





(1)

where

v
=
k
gas
/
k
solid
,


k
so
lid
= thermal conductivity of solid material,


p

= porosity = (ρ
max
-
ρ
matl
)/ρ
max
,

ρ
max

= density of solid material in the porous system,

ρ
matl

= density of the
porous

material,
and


k
gas

= thermal conductivity of gas =
k
cond
+
k
rad

For a spherical pore of
radius
r
, the radiation contribution to the overall thermal conductivity of
the pore
i
s
14
:






(2)

with

σ

=

Stefan
-
Boltzmann constant (5.669
x
10
-
8

W/m
2

K
4
),


E

= emissivity

of solid material

(1.0 for black bodies)
, and


T

= absolut
e temperature (K).

Knowing the
dens
ities of the FR
M and the base solid components (by grinding to a powder and
measuring in an alcohol solution, for instance), one can
calculate the porosity of the FR
M. This,
along with estimate
s

of

the solid’s thermal co
nductivity and

the material’s
typical pore radius
,

and the tabulated thermal conductivity of air as a function of temperature,
3
,1
5

permits the
estimation of the thermal conductivity of the F
R
M at elevated temp
eratures. As shown in
Figures 4

and
5
, applica
tion of this theory to both portland cement
-
based

and gypsum
-
based
spray
-
applied F
R
Ms yields results in good agreement with existing measurements.

While the
measured values of ρ
max

and ρ
matl

were used in the calculations, in each case, the pore radius was

a floating parameter that was adjusted to give a reasonable fit to the experimental data. But, in
each case, the adjusted value for the pore radius is in agreement with visual optical microscopy
observations of the characteristic pore sizes in these mate
rials

(Figures 6 to 8)
. These figures
illustrate the potential of applying this approach in lieu of or to minimize the number of
complicated and costly high temperature measurements for these materials
. The approach also
points out the advantage of incor
porating
smaller pores into the F
R
M structure, as the insulating

7

performance of materials with larger ones will suffer
significantly
due to radiation effects at
higher temperatures.


Figure
4
: Measured thermal conductivities
1

and predictions base
d on theor
y of Russell/Loeb
1
1
,1
4

for
two similar portland
cement
-
based
spray
-
applied
F
R
Ms.



Figure 5
: Measured thermal conductivities
1

and predictions based on theory of Russell/Loeb
1
1
,1
4

for a gypsum
-
based
spray
-
applied
FR
M.




8

Figure 6: Optical micrograph for po
rtland

cement
-
based spray
-
applied F
R
M
-
A. Typical pore
diameter

as indicated by the
labeled
scale bar
s

i
n the
middle

of the
two
images is on the order of
1.0 mm

corresponding to a pore radius of 0.5 mm
. The original image is on the left and a
contrast
-
enh
anced version that better highlights the porosity is shown on the right.




Figure 7: Optical micrograph for portla
nd
cement
-
based spray
-
applied FR
M
-
B. Typical pore
diameter

as indicated by the label
ed scale bar
s

i
n the
m
i
d
d
l
e of the
two
images is on t
he order of
1.5 mm

corresponding to a pore radius of 0.75 mm
. The original image is on the left and a
contrast
-
enhanced version that better highlights the porosity is shown on the right.




Successful application of this theory requires a detailed unde
rstanding of the dynamic
microstructure of the FRM. For example, one widely used spray
-
applied FRM utilizes expanded
polystyrene (EPS) beads as a lightweight aggregate. When these
highly porous
beads burn out at
elevated temperatures,
even though the tot
al porosity will not change significantly,
a new larger
size of characteristic pores will be created within the microstructure, potentially leading to an
increase in thermal conductivity. Intumescents will also be a challenging application, as
in this
cas
e, the pore size and total porosity are both

dynamic variable
s

that change dramatically during
the fire exposure and charring of the coating.



A more detailed microstructural analysis is possible via the utilization of x
-
ray
microtomography which can capt
ure the three
-
dimensional microstructure of materials with a
voxel dimension on the order of micrometers.
16

Example two
-
dimensional images (slices)

9

obtained for both gypsum
-
based and portland cement
-
based FRMs using one of the X
-
ray
microtomography units
available at the Center for Quantitative Imaging at Pennsylvania State
University are provided in Figure 9.


qhese= 摩gital= image
J
扡se搠 three
J
摩mensi潮al=
micr潳tructures= can= 扥= segmente搠 int漠 s潬i搠 an搠 灯pe= 灨asesⰠ an搠 finite= element= an搠 finite=
摩fference=
techni煵es= a灰pie搠 t漠 c潭灵te= their= e煵ivalent= thermal= c潮摵ctivityK
17

For example, a
numerical temperature gradient could be placed across the microstructure and the computed heat
flow used to determine the thermal conductivity of the composite 3
-
D micro
structure. Thus, this
approach is similar to that used in conventional computational thermal analysis, but it is being
applied at the microstructure scale instead of the conventional macro (structure) scale.


Figure 8: Optical micrograph f
or gypsum
-
based
spray
-
applied FR
M
-
C. Typical pore
diameter

as indicated by the labeled scale bars
i
n the
m
i
d
d
l
e of the images is on the order of 0.4 mm

corresponding to a pore radius of 0.2 mm
. The original image is on the left and a contrast
-
enhanced version that bette
r highlights the porosity is shown on the right.




Recommended Procedures



A recommended approach for supplying the thermophysical properties needed by thermal
performance models is

the following
:

1) density


determine density via the concurrent meas
urement of mass and dimensional changes
using thermogravimetric and thermal expansion measurements,

2) heat capacity


determine heat capacity as a function of temperature using the largest readily
available sample cell and a STA unit, and following the AS
TM E1269 protocols,
2

3) enthalpies of reaction


compute enthalpies based on the mass loss (TGA) measurement and
the calculated enthalpies of reaction based on a detailed knowledge of the FRM and its thermal
decomposition (these calculations can be critica
lly examined by comparison with analysis of the
endotherms and exotherms in the STA results), and

4) thermal conductivity


supplement direct “low” temperature thermal conductivity
measurements with detailed characterization of the microstructure of the FR
M (porosity and pore
size) and application of the theory of Russell (or other equivalent) to provide high temperature
estimates.






Certain commercial products are identified in this paper to specify th
e materials used and procedures employed. In
no case does such identification imply endorsement by the National Institute of Standards and Technology, nor does
it indicate that the products are necessarily the best available for the purpose.


10

Figure 9: Example
s of

two
-
dimensional images from three
-
dimensional microtomography data
sets for gypsum
-
based (left) and
mine
ral fiber/
portland cement
-
based (right) F
R
Ms. Materials
were imaged in a p
olypropylene

tube with a nominal inner diameter (ID) of 27 mm.





A Word of Caution about Aging Tests


One of the action items that came out of the initial FEMA study
18

of the c
ollapse of the
W
orld
T
rade
C
enter

was that the durability of F
R
Ms is a little
-
considered but critically important
component of their long term performance. In response
to this, Underwriters Laboratories
, along
with the F
R
M industry and end users, are

deve
loping a draft standard t
o assess the durability of
FR
Ms
1
9
, based on their existing evaluations of intumescent coatings for outdoor use. The basic
procedure is to expose the F
R
M to some aging environment and then verify through thermal
exposure
(fire)
tes
ting that the performance of the aged material is at least equivalent to a
specified percentage of
that of
the original material. Performance is generally assessed in terms
of the time
that
it takes a steel (duct) pipe protected with the F
R
M to reach a sp
ecific temperature
(typically 538
o
C) when exposed to a standard temperature rise curve “fire environment”.

In
developing these durability exposures, care must be taken that the exposure conditions are both
reasonable and applicable to the various classes

of spray
-
applied F
R
Ms. F
or example, as shown
in Figure 10
, the current practice of exposing intumescents to a temperature of 70
o
C for 270
days can result in considerable mass loss for other types of spray
-
applied F
R
Ms
, even for much
shorter exposures of

two to three months

(
particularly those based on gypsum

binders
)
. Since
the loss of water due to dehydration during a fire exposure is one of the mechanisms by which
these materials “insulate” the steel substrate, it would be expected that these “aged” m
aterials
would exhibit a
n

inferior performance in comparison to their original counterparts.

But, is it the
material performance or the
ag
ing conditions that should be called into question?

When
moisture is added to the aging exposures, the degradation
m
ay
become even greater for
conventional fibrous insulating materials.
20





11

Figure 10
: M
ass loss
(fraction)
up
on long term
(two

month

to three month)
oven

exposure to
different temperatures for gypsum
-
based

(FR
M
-
D) and portland cement
-
based (
F
RM
-
E) FR
Ms

(sa
mple size of

3 g)
.



Acknowledgements


The authors would like to thank Dr. Phillip M. Halleck and Dr. Abraham S. Grader of the
Center for Quantitative Imaging, Pennsylvania State University, for supplying the
microtomographic images shown in Figure 9.


References:


1)
Anter Laboratories, Inc., Transmittal of Test Results, report to NIST, 2004.

2)
ASTM Annual Book of Standards
;

ASTM

International
:

West Conshohocken, 2004.

3
)
CRC Handbook of Chemistry and Physics
, 68th Edition;

CRC Press
:

Boca Raton
, 1987.

4
)
Smith JM,

Van Ness HC
. Introduction to Chemical Engineering Thermodynamics
;

McGraw
-
Hill Book
Co.
:

New York, 1975.



5
) Thomas G.
Fire Mater
.
2002;
26
:
37.

6
) Taylor HFW.
Cement Chemistry
;

Thomas Telford
: London
, 1997.



7
) Hansen

PF, Hansen J, Hougaard KV, Pedersen
EJ. "Thermal Properties of Hardening Cement Paste,"
Proc. RILEM Int. Conf. on Concrete at Early Ages
; RILEM:

Paris
, 1982, p. 23.

8
)

Flynn DR. “Response of High Performance Concrete to Fire Conditions: Review of Thermal Property
Data and Measurement Techniq
ues,” NIST GCR
99
-
767
, U.S. Department of Commerce,
March 1999.

9
) Gustafsson SE.
Rev. Sci. Instrum
.
1991;
62
:
797.

10
) Log T, Gustafsson SE.
Fire Mater
. 1995;
19
:43.

11
)

Russell HW.
J
.

Amer
.

Ceram
.

Soc
. 1935;
18
:1.

12
) Frey S.
Z. Elektrochem
.

1932;
38
:260
.

13
) Bruggeman DAG.
Ann. Der Phys
.

1935;
24
:636
.

14
)

Loeb AL.
J. Amer. Ceram. Soc
. 1954;
37
:96
.

15
) Holman JP.
Heat Transfer
;

McGraw
-
Hill Book Co.
:

New York, 1981.

16
) Bentz DP, Mizell S, Satterfield S, Devaney J, George W
, Ketcham
P, Graham J, Porterfiel
d J,
Quenard D, Vallee F, Sallee H, Boller E, Baruchel J,
J
.

Res
.

NIST

2002;
107
:137.


12

17
) Garboczi EJ
.

“Finite Element and Finite Difference Programs for Computing the Linear Electric and
Elastic Properties of Digital Images of Random Materials,” NISTIR
62
69
, U.S. Department of
Commerce, December 1998.

18
) FEMA 403, “World Trade Center Building Performance Study: Data Collection, Preliminary
Observations, and Recommendations,” Federal Emergency Management Administration, Washington,
DC, May 2002.

1
9
) Standa
rd for Durability Tests for Fire Resistive Materials Applied to Structural Steel, UL 2431, Draft
1.1, Underwriters Laboratories Inc., Northbrook, IL, 2003.

20
) Low N
MP
.

“Material Degradation of Thermal Insulating Mineral Fibers,” Thermal Insulation:
Materi
als and Systems, ASTM STP
922
, F.J. Powell and S.L. Matthews, Eds., American Society for
Testing and Materials
:

Philadelphia, 1987
;

p. 477.


13

Presented at ASCE/SEI Structures Congress, New York, April 2005.

Microstructure and Materials Science of Fire Resistive Materials


Dale P. Bentz
1
, Phillip M. Halleck
2
, Michelle N. Clarke
1
, Edward J. Garboczi
1
,

an
d Abraham S. Grader
2


1
Building and Fire Research Laboratory, National Institute of Standards and Technology, 100
Bureau Drive Stop 8615, Gaithersburg, MD 20899
-
8615;

PH (301) 975
-
5865; FAX (301) 990
-
6891; e
-
mail:
dale.bentz@nist.gov

2
Center for Quantitative Imaging, The Pennsylvania State University, University Park, PA
16802
-
5000; PH (814) 863
-
1701; FAX (814) 865
-
3248;

e
-
mail:
phil@pnge.psu.edu



Abstract



Fire resist
ive materials (FRMs) are a critical component in the design of safe buildings.
Current performance testing is strongly based on the ability of the FRM to adhere to and to
control the temperature rise of its substrate. A fundamental understanding of the m
icrostructure
and performance properties of these materials is sorely needed to model their performance in real
world systems and scenarios. While room temperature properties are more easily evaluated, it is
the high temperature properties of the material
s that are critical to performance during an actual
fire. This paper will describe preliminary efforts in an experimental/computer modeling program
being conducted at NIST to apply a materials science approach to characterizing the
microstructure and prop
erties of these materials. Three
-
dimensional x
-
ray microtomography is
applied to obtain a representation of the microstructure of the materials. These microstructures
can then be analyzed quantitatively to characterize critical parameters such as porosit
y and pore
sizes, and the effects of these parameters on properties such as thermal conductivity. This
analysis, along with characterization of the density and heat capacity of the FRM as a function of
temperature, will provide the inputs needed for therm
al performance models.


Introduction



Fire resistive materials (FRMs) perform a critical function in building safety by
protecting steel components from high temperature conditions during a fire or multi
-
hazard
exposure. These materials generally delay t
he transfer of energy from the ongoing fire to the
steel via a combination of a low thermal conductivity and a variety of endothermic reactions,
such as dehydration and decarbonation of cementitious and gypsum
-
based binders. In addition
to heat transfer t
hrough the FRM by conduction, at higher temperatures, transfer by radiation
also makes a substantial contribution to material performance. Radiation transfer in a porous
material is influenced by both overall porosity and by the size and shape of the indi
vidual
“pores” (Russell, 1935; Loeb, 1954).


Currently, FRMs are evaluated and certified based mainly on their ability to limit the
temperature rise of the substrate steel when exposed in a furnace to a standard temperature rise
curve (ASTM E119; ASTM, 200
4). The FRMs are thus rated for a specific period of time for
protecting a specific member of the steel construction, e.g., a 2 h rating for protecting beams or a
3 h rating for protecting columns. The E119 test is strictly pass/fail and as such does not

truly

14

quantify material performance. Furthermore, it is extremely difficult to extrapolate E119 test
results to real fire scenarios. Clearly, the development of new FRMs and an increased
understanding of the thermal performance of existing ones would be
nefit greatly from a
materials science
-
based approach to characterizing these materials.


Recently (Bentz et al., 2004), it has been suggested that to characterize FRMs with respect to
thermal performance models, measurements/calculations of the followin
g thermophysical
properties are required: thermal conductivity, density, heat capacity, and any enthalpies of
reactions or phase changes occurring in the temperature range of interest. This paper focuses on
a computational approach to estimating thermal c
onductivity based on a detailed analysis of the
three
-
dimensional microstructure of the FRMs. Such an approach may provide a viable
alternative to the expensive and often difficult measurement of thermal conductivity at elevated
temperatures for these dyn
amic materials. Additionally, the approach should provide valuable
insights into the microstructural features that most influence thermal performance, so that
existing products may be optimized and new ones formulated with minimal effort.


The basic appro
ach is to capture the three
-
dimensional microstructure of FRMs at sub
-
millimeter
resolution using x
-
ray microtomography. Image processing and finite difference computer
programs are then utilized to extract the key microstructural features (pores) and det
ermine their
influence on the thermal conductivity as a function of material temperature. Finally, the
computational results are compared to experimental measurements performed on the same
materials to both evaluate the accuracy of the computational appro
ach and to identify areas
where improvements are needed.


Experimental Procedures



Sprayed parallelepiped samples of the following FRMs were obtained from their
manufacturers: one FRM with a gypsum binder and two FRMs containing mineral fibers with a
bind
er based on portland cement. Samples of each material were sent to a private testing
laboratory (Anter Laboratories, 2004) for experimental measurement of their thermal
conductivities as a function of temperature using a standard hot wire technique (ASTM,

2004).
The testing laboratory reported their results for thermal conductivity to be normally within
±

3
%. For each material, nominal 25 mm (1”) diameter cylindrical cores were carefully extracted
using a utility knife. The cores were then placed in 27

mm inner diameter (ID) polypropylene
tubes and mounted for viewing by the x
-
ray microtomography system at the Center for
Quantitative Imaging at the Pennsylvania State University

K
=
=
s潬umetric=
x
J
ray= Cq= 摡ta= were=c潬lected
=
using
=
the=facilityDs=micr潦潣us=
x
J
ray=s潵rce=at=a=v潬tage=
setting=潦=
ㄸN
=
歖=
an搠a=l潷=tu扥=current=潦=㔰R
μ
A

to minim
i
ze focal spot size
and
thus optimiz
e

spati
a
l resolution
.

We positioned the sample in the gantry to magnify the sample,
and
calibrated
the resulting voxel dimensions

against a dimensional standard
for precision and to allow
combining adjacent d
ata sets without overlapping or skipping portions of the sample volume
.







Certain com
mercial products are identified in this paper to specify the materials used and procedures employed. In
no case does such identification imply endorsement by the National Institute of Standards and Technology, nor does
it indicate that the products are ne
cessarily the best available for the purpose.


15

Because of the different microstructures present in the two types of FRMs examined in this study
(e.g., characteristic feature dimensions), the microtomography data sets were acquir
ed with
different voxel dimensions. The microtomography data sets for the gypsum
-
based FRM were
acquired with voxel dimensions of dx =dy =0.0273 mm and dz =0.0361 mm
.

Each data set
consisted

of a 1024 x 1024 x

7
50

array of 16
-
bit
x
-
ray absorption values on an arbitrary scale.
For th
is

sample we collected approximately 750 slices covering a volume about 28 mm long by
28 mm in diameter.
For the fiber/cement
-
based FRMs,

in order to cover a large
r

representative
s
ample volume,
the
magnification

was reduced

by repositioning the
s
ample between the source
and
the
detector
,
result
ing in voxel dimensions of dx =dy =0.0586 mm and dz =0.0740 mm,
for

data arrays
512 pixels by 512 pixels

by 492
.
Thus, t
he data cover sampl
e volumes
about
36 mm
long by 30 mm in diameter.
Each individual two
-
dimensional slice was available as a
16
-
bit
tiff
-
format image for further processing as described below.


Computational Procedures



The three
-
dimensional FRM microstructure data sets we
re processed using the following
computational procedures:

1)

segmentation into binary images
-

utilizing the commercially available Image Pro
software package, each two
-
dimensional FRM slice image was segmented into a binary
image of “pores” and “solids” by
manually choosing a greylevel threshold; the chosen
threshold was held constant for all of the two
-
dimensional slices comprising each FRM
material but varied between the three different materials, due to inherent contrast
variations.

2)

extraction of a subvol
ume
-

a 200 by 200 by 200 voxel subvolume was extracted from
each three
-
dimensional data set; in each case, the subvolume was chosen away from the
sample edges and in an attempt to select as representative a volume of the overall
material as possible.

3)

isola
tion of pores and quantification of pore volumes
-

each binary subvolume data set
was further analyzed to identify individual pores and determine their volumes (by voxel
counting); computer programs were written in the C programming language to perform
pore

separations utilizing such common image processing algorithms as erosion/dilation
and watershed segmentation (Russ and Russ, 1988).

4)

prediction of thermal conductivity
-

the processed subvolumes were used as input into a
finite difference program (Garboczi,

1998) to estimate the thermal conductivity of the
composite FRMs based on an electrical analogy; a voltage (temperature) gradient was
placed across the microstructure and the resulting currents (heat flows) were computed
for each microstructure element (n
ode).


To utilize the finite difference program, it is necessary to assign thermal conductivities to the
“pore” and “solid” components of the underlying microstructure. Knowing the pore volume of
each individual pore, equivalent radii were calculated assu
ming a spherical pore geometry.
Then, the thermal conductivity of a pore of radius
r

at material temperature
T

was given by:






(1)

where:

k
gas

= thermal conductivity of air at temperature
T,
and according to (Loeb, 1954),


16






(2)

with

r

= pore radius (m),

σ

= Stefan
-
Boltzmann constant (5.669x10
-
8

W/m
2
•K
4
),


E

= emissivity of solid material (1.0 for black bodies), and


T

= absolute temperature (K).

In this way, each different size pore in the three
-
dimensi
onal microstructure was assigned a
different thermal conductivity value.


When considering the “correct” thermal conductivity to assign to the “solids”, several
complications arise. First, while the microtomography clearly indicates the coarser pores (50
μm
to 100 μm and greater in diameter) present in the microstructure, the remaining solid phases are
themselves porous. While it may have been possible to estimate the local “micro
-
porosity”
based on the greylevel intensity at each solid voxel in the three
-
dimensional microstructure,
instead, a single “fine” porosity value within all solid voxels was estimated based on the
measured densities of the original FRMs, the measured densities obtained by grinding them to a
fine powder (hopefully removing all inter
nal porosity), and the microtomography
-
measured
coarse porosity volume fraction for each material. Then, the theory of (Russell, 1935) was used
to estimate the thermal conductivity of the porous solid component of the microstructures,
k
ps
, as:





(3)

where

v
=
k
pore
/
k
solid
,


p

= porosity of the “solid” voxels,

k
solid
= thermal conductivity of solid (powder) material, and


k
pore

= thermal conductivity of pores in the “solid” voxels =
k
gas
+
k
rad

For calculations of
k
rad

for equation

(3), an upper bound pore diameter equal to the smallest of
the voxel dimensions was chosen for each material (e.g., 0.0273 mm or 0.0586 mm). The
thermal conductivities of the solid powders,
k
solid
, were chosen as 0.8 W/m•K for the gypsum
-
based FRM and 0.
4 W/m•K for the fiber/cement
-
based FRMs, to provide predictions in
agreement with the room temperature measured values of thermal conductivity (Anter
Laboratories, 2004). In applying the theory of Russell, the density (porosity) of the porous
material was

adjusted to account for its measured mass loss as a function of temperature. The
gypsum
-
based FRM loses about 25 % of its mass upon heating to 1000
o
C, while the
fiber/cement
-
based FRMs lose between 10 % and 15 % (Anter Laboratories, 2004).


For the gyps
um
-
based FRM, a further complication is that the thermal conductivity of anhydrite
(dehydrated gypsum) is nearly four times that of gypsum (Horai, 1971). Based on the measured
mass loss of the gypsum
-
based FRM and utilizing the Hashin
-
Shtrikman upper and
lowers
bounds for thermal conductivity (Hashin and Shtrikman, 1962), it was estimated that upon
complete conversion of the gypsum to anhydrite, the thermal conductivity of the solid FRM
powder should increase to be on the order of 1.66 W/m•K. Thus, for te
mperatures above the
nominal dehydration temperature for gypsum of about 300
o
C, the finite difference computations
were performed with
k
ps

values based on both gypsum and anhydrite for comparison to
experimental data.




17

Results



Figure 1 illustrates the

microstructural features captured by the x
-
ray microtomography
for the two types of FRMs. For the gypsum
-
based material on the left, one can easily observe
plate
-
like vermiculite particles surrounded by a porous gypsum binder. For the fiber/cement
-
based

FRM on the right, substantially larger pores are observed. The bright “particles” observed
in this image are most likely agglomerations of the cement particles that are bonding together
fibrous subregions of the microstructure. As observed more clearly
in the three
-
dimensional
representations of microstructure provided in Figures 2 and 3, while the pores in the gypsum
-
based FRM definitely appear to be comprised of closed roughly spherical shapes, those in the
fiber/cement
-
based FRM may be interconnected
across large regions of the microstructure.
These differences in pore shape/connectivity would also be expected to influence the thermal
conductivities of these two materials, particularly at elevated temperatures.




Figure 1. Two
-
dimensional x
-
ra
y microtomography images from a gypsum
-
based FRM
(left: 28 mm by 28 mm) and a fiber/cement
-
based FRM

(right: 30 mm by 30 mm), illustrating some of the differences in microstructural features.




Figure 2. Renderings of the three
-
dimensional x
-
ray microt
omography original data sets
(100 by 200 by 200 voxels with a 100 by 100 by 100 voxel volume removed for increased
visual clarity) for a gypsum
-
based FRM (left) and a fiber/cement
-
based FRM (right).
Pores are dark and “solid” regions are bright.


18



Figure 3. False color renderings of the individual pores isolated using the watershed
segmentation algorithm in a gypsum
-
based FRM (left: 120 by 120 by 120 voxels) and a
fiber/cement
-
based FRM (right: 200 by 200 by 200 voxels).


The thermal

conductivity predictions and measurements for the gypsum
-
based FRM are
provided in Figure 4. While good agreement between the experimental results and the
computational predictions is observed for temperatures below 300
o
C, above this temperature the
gyp
sum
-
based predictions underestimate the measured values while the anhydrite
-
based
predictions generally overestimate the measured values, although providing a reasonable fit for
temperatures above 600

o
C. This could indicate that (during the experime
ntal measurement of its
thermal conductivity) in the intermediate temperature range of 300
o
C to 600
o
C, the FRM
possibly contained a mixture of gypsum (hemihydrate) and anhydrite. These results highlight
one of the inherent difficulties in equitably meas
uring the thermal conductivity of FRMs at
elevated temperatures, the fact that their mass, their chemical composition, and their
microstructure may all be changing during the course of the measurement.


The importance of pore size in controlling high tempe
rature thermal conductivity is indicated by
the results shown for the first of the fiber/cement
-
based FRMs in Figure 5. Here, because of the
non
-
spherical shape of many of the pores, the watershed segmentation algorithm subdivided the
largest porous “regi
ons” into

two or more individual pores. In this case, better agreement with
the experimental data was observed for the three
-
dimensional microstructure where the pores
were identified by the simple application of a burning algorithm without any applicatio
n of
erosions/dilations to the binary image subvolume. As illustrated in Figure 6, similar results were
observed for the second fiber/cement
-
based FRM, where larger thermal conductivities are
observed at the highest measured temperatures due
to both an in
creased porosity and a generally
larger pore size.


A large degree of anisotropy in the three
-
dimensional subvolumes was observed for these FRMs,
as indicated by the large difference between the computed thermal conductivities for the (x and
y) direction
s and the z direction. In Figure 3, several large flat plate
-
like porous regions oriented



19


Figure 4. Measured and predicted thermal conductivities for a gypsum
-
based FRM as a
function of temperature, for the case where individual pores were identified

using a
watershed segmentation algorithm (Russ and Russ, 1988).



Figure 5. Measured and predicted thermal conductivities for the first fiber/cement
-
based
FRM as a function of temperature.


in the xy (spraying) plane are clearly observed to comprise a maj
or fraction of the subvolume. It
should be noted that the three
-
dimensional box in Figure 3 has been rotated to better view these
pores and that the z
-
direction moves from left to right in the labeled subvolume. Furthermore,
for these materials, it must
also be noted that some of the underestimation of the experimental
results is likely due to energy transfer through the FRMs by radiation transmission and scattering


20


Figure 6. Measured and predicted thermal conductivities for a second fiber/cement
-
based
FRM as a function of temperature.


(Flynn and Gorthala, 1997), due to their overall fibrous nature and likely percolated three
-
dimensional pore networks. The theory of Loeb (Loeb, 1954) d
oes not account for this mode of
radiation transport through the porous material, as it assumes a porous solid comprised of
isolated (not interconnected) pores.


Conclusions



The procedures and results presented indicate the viability of utilizing microst
ructural
characterization and computation to estimate the thermal conductivity of FRMs at elevated
temperatures. However, the computational procedures can not be applied blindly, due to the
many complicating factors present in these materials. It is only

with a detailed understanding of
the microstructural components of these materials and their changing nature with increasing
temperature that truly adequate predictions can be envisioned. The influences of total porosity
(or equivalently density), pore s
ize, and pore connectivity on heat transfer were all highlighted in
the current case studies.


Acknowledgements



The authors would like to thank Mr. John Winpigler of BFRL/NIST for measuring the
powder densities of the various FRMs.


References


Anter Lab
oratories, Inc. (2004). “Transmittal of Test Results.” report to NIST.

ASTM (2004),
ASTM Annual Book of Standards
, ASTM International, West Conshohocken.


21

Bentz, D.P., Prasad, K.R., and Yang, J.C. (2004). “Towards a Methodology for the Characterization of
F
ire Resistive Materials with Respect to Thermal Performance Models.” submitted to
Fire and
Materials.

Flynn, D.R., and Gorthala, R. (1997). “Radiation Scattering Versus Radiation Absorption
-

Effects on
Performance of Thermal Insulation Under Non
-
Steady
-
Sta
te Conditions.”
Insulation Materials:
Testing and Applications: Third Volume, ASTM STP 1320
, American Society for Testing and
Materials, West Conshohocken, PA, 366
-
380.

Garboczi, E.J. (1998). “Finite Element and Finite Difference Programs for Computing the

Linear Electric
and Elastic Properties of Digital Images of Random Materials.” NISTIR 6269, U.S. Department
of Commerce.

Hashin, Z., and Shtrikman, S. (1962). “
A Variational Approach to the Theory of the Effective Magnetic
Permeability of Multiphase Mater
ials
.”

J. Appl. Phys
., 33, 3125
-
3131.

Horai, K. (1971). “Thermal Conductivity of Rock
-
Forming Minerals.”
J. Geophys. Res.
, 76(5), 1278
-
1308.

Loeb, A.L. (1954). “Thermal Conductivity: VIII, A Theory of Thermal Conductivity of Porous
Materials.”
J. Am. Ceram
. Soc.
, 37, 96
-
99.

Russ, J.C., and Russ, J.C. (1988). “Improved Implementation of a Convex Segmentation Algorithm.”
Acta Stereologica,
7(1), 33
-
40.

Russell, H.W. (1935). “Principles of Heat Flow in Porous Insulators.”
J. Am. Ceram. Soc
., 18, 1
-
5.


2
2

Submitte
d to Fire and Materials (2004)

A Slug Calorimeter for Evaluating the Thermal Performance of Fire Resistive Materials


D.P. Bentz, D.R. Flynn
§
, J.H. Ki
m
**
, and R.R. Zarr

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899
-
8615


Abstract



The utilization of a slug calorimeter to evaluate the thermal performance of fire resistive
materials (FRMs) is p
resented. The basic specimen configuration consists of a “sandwich”, with
a square central stainless steel plate (slug) surrounded on two sides by the FRM. This sandwich
configuration provides an adiabatic boundary condition at the central axis of the sl
ug plate that
greatly simplifies the analysis. The other four (thin) sides of the steel plate (and FRM
specimens) are insulated using a low thermal conductivity fumed
-
silica board. Metal plates
manufactured from a high temperature alloy, with eight holes

for retaining screws, are placed on
the exterior surfaces of the FRMs to provide a frame for placing the entire sandwich specimen
slightly in compression. The entire configuration is
centrally

placed at the bottom of an
electrically
-
heated box furnace an
d the temperatures of the metal slug and exterior FRM surfaces
are monitored during multiple heating and cooling cycles. Knowing the heat capacities and
densities of the steel slug and the FRM, an effective thermal conductivity for the FRM can be
estimate
d. The effective thermal conductivity of the FRM will be influenced by its true thermal
conductivity and by any endothermic or exothermic reactions or phase changes occurring within
the FRM. Preliminary tests have been conducted on two commonly used FRMs

and on a non
-
reactive fumed
-
silica board to demonstrate the feasibility of determining high temperature
thermal conductivities using this method. This small scale furnace test can potentially be related
to a standard ASTM E119 testing configuration by de
termining the time necessary for the steel
slug to reach a specific “failure” temperature (e.g., 538
o
C).


Introduction



Fire resistive materials (FRMs) are currently generally evaluated using the ASTM
standard test method E119.
1

This test provides a ti
me “rating” for which the FRM will
adequately protect a specific element or subsystem of a structure. Two of the major criteria
determining the performance of a FRM are the measured average and maximum temperatures of
a series of thermocouples placed on t
he (steel) substrate. While useful as practical failure
criteria, these data alone provide little insight into the key thermal properties of the FRM that
would allow a better understanding of its performance. The thermal performance of the FRM is
control
led by its heat capacity, density, thermal conductivity, and any heat released, absorbed, or
transported due to chemical reactions (dehydrations, etc.) and phase changes.
2

The goal of this
paper is to present an experimental setup that maintains the “spir
it” of the ASTM E119 test setup



§

MetSys Corporation, Millwood VA 22646
-
0317.

**

Photonics System Team, Korea Photonics Technology Inst., #459
-
3 Bonchon
-
Dong, Buk
-
Gu, Gwangju, 500
-
210
Republic of Korea.



23

while providing detailed data on the fundamental thermophysical properties and thermal
performance of the FRM.



The key components extracted from the ASTM E119 testing are that a steel substrate is
protected by a specific t
hickness of FRM material and is exposed to a controlled temperature
-
time environment in a furnace. The test specimen size is reduced from the ASTM E119 testing
to a square 152 mm by 152 mm specimen that is nominally 25 mm in thickness. Thermocouples
are
placed in the steel substrate and also at the “exposed” surfaces of the FRMs to monitor
dynamically the temperature gradient that exists across the sample. Additionally, by using a
“sandwich” specimen configuration and a central stainless steel plate of k
nown mass and thermal
properties, the heat flow through the FRM specimens can be easily estimated from a simple
energy balance, taking advantage of the adiabatic boundary condition that exists at the central
axis of the steel plate slug. Knowing the heat
flow and the temperature gradient, an “effective”
thermal conductivity for the FRM as a function of temperature can be determined. This effective
thermal conductivity will be influenced by the true thermal conductivity of the material, any
endothermic or
exothermic reactions occurring in the FRM, and any additional energy/mass
transport due to vaporization of water (steam) and other reaction products formed from
dehydration, decarbonation, etc. of the FRM material. The influence of these reactions can be
conveniently explored by exposing the sandwich specimen to multiple heating/cooling cycles, as
the reactions will likely be present only during the first heating cycle. This approach is presented
in more detail in the sections that follow. A somewhat sim
ilar approach for determining an
effective thermal conductivity of intumescent coatings using a cone calorimeter and numerical
analysis has been presented recently.
3


Experimental


Slug Design


An AISI Type 304 stainless steel plate 152 mm by 152 mm was cu
t from a sheet having a
thickness of 12.7 mm. To monitor the temperature of the steel slug, three vertical holes 3.5 mm
in diameter were milled into the plate along its central axis, extending 51 mm, 76 mm, and 102
mm into the plate’s depth. The holes we
re located at distances of 51 mm, 76 mm, and 102 mm
from the plate’s edge as shown in Figure 1. The steel plate mass was 2340 g. A density value of
8000 kg/m
3

for 304 stainless steel was taken from the literature
4
, along with heat capacity values
as a fu
nction of temperature
5
, as shown in Figure 2. Before testing any specimens, the steel plate
was heated to a temperature of 700
o
C during two separate runs in the furnace. The plate can be
optionally fitted with two allen screws (one on each side) to enab
le the final sandwich specimen
to be suspended from an external balance on two wires. Care must be taken to assure that the
wire diameter is sufficient to support the dead load during the temperature rise experienced
during an actual test run. For our pu
rposes, 16 gauge Chromel
††

wire has 扥en f潵n搠t漠扥
sufficientⰠwhile ㈴2gauge wire resulte搠in tw漠灲emature failures 摵ring 灲eliminary testsⰠwith a
t潴al l潡搠潮 the 潲摥r 潦 㔰〰5g⸠ O灴i潮allyⰠthe final san摷ich c潮figurati潮 can 扥 set in the
††††††††††††††††††††
††††

††

Certain commercial products are ident
ified in this paper to specify the materials used and procedures
employed. In no case does such identification imply endorsement by the National Institute of Standards
and Technology, nor does it indicate that the products are necessarily the best availab
le for the purpose.



24

botto
m center of the (bottom loading) box furnace, as shown in Figure 3, if only temperatures
and not mass are to be monitored during the test.


Figure 1
-

Design of the steel plate slug calorimeter.



Furnace Setup


All experiments
were conducted in an electrically
-
heated box furnace with a working
volume of 360 mm by 360 mm by 360 mm and a maximum operating temperature of 1500
o
C.
The bottom surface of the furnace is located on hydraulic elements and can be moved up and
down for

lo
ading and unloading of specimens (Figure 3). A series of five Type N
thermocouples, insulated for high temperature applications, were introduced into the furnace
through an entry port in the top. The thermocouples were connected to a constant temperature

zone box, where their differential voltages were monitored using a digital multimeter and digital
voltmeter. The thermocouples were monitored periodically and recorded on a computer.
Measurement in ice water yielded an average standard deviation of 0.05

o
C among the five
thermocouples.



152.4 mm

3.45 mm holes at 50.8 mm, 76.2 mm,

and 101.6 mm





12.7 mm

50.8 mm

101.6 mm

152.4 mm


25

Figure 2
-

Literature values
5

and fitted curve for heat capacity of 304 stainless steel. Fitted curve
is of the form
c
p

= A + BT + Cln(T) with T in degrees K.



Figure 3


A completed sandwich specimen of the fumed
-
silica

insulation board mounted and
ready for testing in the box furnace.



FRM and Insulation Materials


Samples of two mineral fiber/portland cement
-
based FRMs were obtained from a
manufacturer. The samples were of nominal size 300 mm by 300 mm by 25 mm. He
at
capacities, densities, and thermal conductivities of these materials had been previously
determined by various laboratories.
2,6,7

Here, the two materials shall be designated as FRM A
and FRM B. The room temperature densities of FRM A and FRM B w
ere measured to be

26

314 kg/m
3

and 237 kg/m
3
, respectively.
6

The heat capacity and mass loss measurements
versus temperature for the
two

materials

are provided in Figures 4 and 5. The testing
laboratory reported their heat capacity values

to be normally within
±

5 %.
6

For each test run in
the furnace, two panels of dimensions 152 mm by 152 mm by 25 mm were cut from the larger
panels to use in the sandwich specimen configuration. The initial mass of each specimen was
measured and recorded
. The specimens of the FRMs were not preconditioned prior to evaluation
in the box furnace.


Figure 4
-

Measured values
6

and fitted curves for heat capacities vs. temperature of the two
FRMs. Fitted curves are of the form
c
p

= A + BT + Cln(T) with T in de
grees K.




A fumed
-
silica insulation board with a low thermal conductivity (

0.02 W/m•K) was
used both as thermal insulation in the sandwich configuration and as a non
-
reactive “reference”
material for evaluating the experimental setup. The board is available as NIST Standard
Reference Material 1449 (http://ts.nist.gov/) and its
room temperature
8

and high temperature
9

thermal conductivities have both been previously measured by NIST. Specimens
8

were obtained
in panels having nominal dimensions of 600 mm by 600 mm by 25 mm with a nominal bulk
density of about 310 kg/m
3
. For the p
urposes of this study, smaller sections were carefully cut as
needed from one large panel using a hand saw. All samples were pre
-
conditioned overnight in a
100
o
C oven prior to being used as insulation or test specimens in the box furnace setup. The
pane
ls had been previously heat treated at 650
o
C for 8 h by the manufacturer.
8

The heat
capacity of the fumed
-
silica board as a function of temperature was measured using a differential
scanning calorimeter (DSC) and the ASTM E1269 standard technique
1

and de
termined to be on
the order of (1000
±
100) J/(kg•K), in good agreement with the limited data available in the
literature for similar materials currently in production.
10,11



Testing Procedure


The specimens and slug plate were surrounded by a 63.5 mm (to
tal thickness), 25.4 mm
wide guard of the fumed
-
silica insulation board and mounted between two Inconel frame plates

(see Figure 3). The entire assembly was held together by a set of eight retaining screws (two on


27

Figure 5
-

Values
6

measured according to A
STM E1131
1

and fitted curves for mass loss vs.
temperature of the two FRMs. Fitted curves are of the form M = A + BT + Cln(T) with T in
degrees K.



each of the four edges of the plates). The assembled sandwich was either suspended from two
wires or sim
ply placed on the bottom center of the box furnace and the thermocouples were
mounted; three Type N thermocouples were placed at the various depths in the center slug plate
and one each was placed on the two exterior surfaces of the specimens being evaluat
ed, between
the specimens and the retaining Inconel plates. In addition to these thermocouples, the
temperatures of the zone box and the furnace were also monitored and recorded. In most tests,
the furnace temperature was programmed to follow a curve sim
ilar to the standard ASTM E119
temperature
-
time curve
1
, but with a less rapid initial temperature rise, due to limitations on the
heating rate of the furnace. The actual temperature
-
time curve employed will be shown in the
results to follow. The tests we
re generally aborted by turning off the furnace power when the
central steel slug reached an average temperature of 550
o
C. However, the thermocouples still
monitored temperatures during cooling. Thus, while the heating portion of the tests generally
occ
urred over a period of 1 h to 2 h, the cooling portion could take as long as 24 h to 48 h, when
the furnace was not opened to accelerate the cooling. Additional tests were conducted at slower
heating rates to determine the sensitivity of the computed ther
mal conductivities to this
parameter. Typically, the furnace temperature was linearly raised to 600
o
C during the course of
either 4 h or 16 h and then held there until the center slug plate also attained nearly this
temperature, at which point the furnac
e was turned off and a cooling curve monitored.


Analysis



Assuming one
-
dimensional heat flow through the FRM components of the specimen
sandwich, a solution will be determined for the case where the temperature of the surfaces of the
exposed specimens is

increasing/decreasing at a constant rate. We consider a pair of FRM
specimens, each of thickness
l,
with the initial condition that the temperature is constant through
the thickness of the specimen and slug, i.e., T(z,0)=0. By symmetry, the mid
-
plane of

the steel
slug plate will be an adiabatic boundary, so that we need only consider one specimen and one

28

half of the steel slug plate. Assuming constant properties, the temperature in the specimen must
satisfy:








(1)


where α=
k/
C

is the thermal diffusivity [m
2
/s],
k

is the thermal conductivity [W/(m•K)],
C
=
ρc
p

is
the volumetric heat capacity [J/(m
3
•K)], and ρ is density [kg/m
3
], all for the FRM specimen
material. The steel slug plate is assumed to have a sufficiently high therma
l conductivity that it
can be considered to be isothermal at any given time. The “thermal capacity” of the slug plate,
per unit area, is taken to be 2
H

= (areal density of the plate)x(heat capacity of the plate), with the
factor of 2 arising from the fact

that we need only consider one half of the steel slug plate. The
thermal capacity,
H
, has units [J/(m
2
•K)].



The boundary condition at the exposed surface of the specimen,
z
=0, is:








(2)


where
F

is the (constant) temperatu
re increase rate having the units [K/s]. The boundary
condition at the specimen surface,
z=l
, which is in contact with the steel slug plate is:







(3)


which follows from the fact that the heat conducted out of this face of the
specimen must equal
the heat absorbed by (one half of) the steel slug plate.



Assuming that the transient (exponentially decaying) terms in the solution, which depend
on the thermal diffusivity of the FRM specimen and time, can be neglected, we arrive at
a
solution of the form:






(4)


The temperature difference across the specimen of the FRM, ∆
T
, is thus:






(5)


Finally, the thermal conductivity of the specimen can be computed as:







(6)


29

If the masses of the slug (M
S
) and FRM specimen (M
FRM
) are known, equation (6) can be
rewritten as:







(7)


where A is the cross
-
sectional area of the slug (or specimen, 0.152 m by 0.152 m = 0.0232 m
2

in
our experimental
setup), and
c
p
S

and
c
p
FRM

refer to the heat capacities of the steel plate and FRM
specimen in units of [J/(kg•K)], respectively. A similar analysis can be performed for the
cooling case (
F
<0,
T(z
,0)=constant), and it can be shown that equation (7) applies

in this case as
well.



Equation (7) was conveniently implemented in a spreadsheet program to determine the
effective thermal conductivity from the acquired temperature
-
time data points. The measured
temperature
-
versus
-
time series for the slug and for
the exterior FRM surfaces were used to
compute the instantaneous values of
F

(

T
/∂
t
) and ∆
T

for use in equation (7). Measured heat
capacities of the 304 stainless steel (Figure 2) and FRMs (Figure 4) as a function of temperature
and mass losses versus temperature for the FRMs (Figure 5) were used to further refine the
parameters us
ed in equation (7). The resulting values of
k

will be graphed against the mean
specimen temperature ([
T
(0,
t
)+
T
(
l,t
)]/2) in the results that follow. While this paper presents
preliminary results to indicate the feasibility of utilizing the slug calorimete
r method to evaluate
the thermal performance and specifically the effective thermal conductivity of FRMs, an
expanded uncertainty analysis could be conducted based on equation (7) and the law of
propagation of uncertainty.
12

Assuming that the heat capacit
ies of the steel slug and the FRM
specimen are fairly well known and that lengths and masses can be measured with less than 1%
uncertainty, the uncertainties in the thermocouple measurements at high temperatures, which are
used to calculate both
F

and ∆
T

i
n equation (7), will be the most significant contributors to the
overall uncertainty. Thus, the uncertainty can be reduced simply by applying equation (7) over a
larger time interval. For example, assuming an optimistic uncertainty of 1
o
C for the
thermo
couple readings at high temperatures, changing the sampling frequency from 1 min to 5
min reduces the estimated uncertainty in the effective thermal conductivity from about 25 % to
about 5 % for thermal conductivities computed in the temperature range of 4
00
o
C to 700
o
C
during heating. During cooling, using a 25 min interval to calculate the effective thermal
conductivity reduces its uncertainty to about 8 % from a value of about 40 % for 5 min intervals.


Results and Discussion


1) Fire Resistive Materia
ls


The individual thermocouple temperatures collected during a single heating/cooling cycle
of FRM A are provided in Figure 6. The ASTM E119 standard temperature
-
time curve
1

is
shown for comparison to the heating curve achievable in the electric furnace.

It is worth noting
that during a portion of the heating curve the exterior FRM surface temperatures actually exceed
the “ambient” temperature of the furnace, most likely due to enhanced radiation transfer between
the Inconel

retaining plates and the indi
vidual furnace elements. This reinforces the need to
center the sandwich specimen in the furnace, so that both sides (specimens) are exposed to
nominally the same thermal environment. There is little variability among the three

30

thermocouples mounted in t
he steel slug, indicating that the assumption that it behaves as an
isothermal slug mass is a generally valid one. Since these three thermocouples are also mounted
at different depths in the steel plate, a low variability among them also supports the vali
dity of
the assumption of one
-
dimensional heat transfer through the FRM that is critical to the
quantitative analysis. In Figure 6, it is clearly observed that even after the furnace is turned off
(as indicated by the peak in the furnace and outer FRM tem
perature curves near 100 min), the
temperature in the steel slug continues to rise due to the thermal inertia (lag) of the system.
When the interior temperature of the slug exceeds the exterior temperature of the FRM, the
direction of the specimen heat fl
ow reverses.


Figure 6
-

Temperature vs. time data for one heating/cooling cycle for FRM A specimens.




One performance criterion that could be conveniently extracted from the data in Figure 6
is the time necessary for the steel slug to reach some specifi
c temperature, such as 538
o
C for
example.
1

For the initial heating cycle of FRM A shown in Figure 6, approximately 105 min
were required for the steel slug to achieve this temperature. For two subsequent heating cycles,
these times were observed to be o
n the order of 110 min. These results suggest that most of the
performance of this particular FRM is achieved via its “low” thermal conductivity and not via
the contribution of significant endothermic reactions, as will be discussed in more detail when
th
e computed thermal conductivity curves are presented below.



Equation (7) was applied to the data shown in Figure 6 and the computed thermal
conductivity values for five different heating/cooling cycles are provided in Figure 7 in
comparison to the previo
usly measured values. One of the testing laboratories reported their
results for thermal conductivity to be normally within ± 3 %.
6

The first three heating cycles
followed the furnace heating curve shown in Figure 6. For the fourth and fifth heating cyc
les, as
outlined above, the furnace temperature was ramped to 600
o
C in 4 h and 16 h, respectively. The
cooling curves for the third and fourth cycles are incomplete due to power outages that occurred
during the course of these experimental runs. The co
mputed thermal conductivity values
agree with the values measured previously using either a hot wire
6

(ASTM C1113
1
) or a

31

transient plane source (TPS) method
7,13

to within 15 % for temperatures up to 600
o
C. The
computed values at temperatures abov
e 600
o
C for the first three heating cycles are clearly higher
than those previously measured, which could be due to enhanced heat transfer by radiation in
these highly porous fibrous materials
14

sandwiched between the “radiating” exterior Inconel
plates a
nd the interior steel slug. It is observed that, after the initial transients, the data for the
five different cooling curves are all quite similar, indicating that an equilibrium had been reached
within the FRM with respect to reactions after the first h
eating cycle.


Figure 7


Effective thermal conductivity results for FRM A in comparison to measured data.
6,7




A comparison of the heating curves is even more informative. The differences among the
heating curves for the first and the two subsequent r
uns should be indicative of the reactions, etc.
occurring in the FRM. In the data in Figure 7, two phenomena appear to be contributing to these
differences. First, there is an endothermic contribution, most likely due to dehydration of the